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GRE · Practice Sheet 42

Sheet code: GRE-S42 · 20 questions

Name: ______________

Date: ______________

1.
Mathematics
Find term number 4 of a geometric progression with first term 4 and common ratio 2.
Formula:GP nth Term
$a_n = a\,r^{\,n-1}$
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2.
Mathematics
If f(x) = 2x³ + 5x² + 2x, find f′(5).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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3.
Quantitative Aptitude
In how many ways can 2 objects be chosen from 10 distinct objects? (Find ⁿᴄᵣ for n = 10, r = 2.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
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4.
Quantitative Aptitude
Two fair dice are rolled. What is the probability that the sum of the numbers is 4?
Formula:Probability (two dice)
$P = \dfrac{\text{favourable}}{\text{total}}$
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5.
Quantitative Aptitude
A value changes from 600 to 750. Find the percentage increase.
Formula:Percentage Change
$\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$
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6.
Mathematics
For the quadratic 1x² − 7x + 0 = 0, find the sum and product of its roots.
Formula:Vieta's Formulas (roots)
$\alpha+\beta=-\dfrac{b}{a},\;\alpha\beta=\dfrac{c}{a}$
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7.
Mathematics
Find the sum of the first 20 terms of an AP with first term 3 and common difference 7.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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8.
Quantitative Aptitude
An item is bought for $600 and sold for $660. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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9.
Mathematics
Evaluate ∫ from 2 to 4 of 1x^2 dx.
Formula:Definite Integral of a Power
$\int_{p}^{q} a x^{n}\,dx = \dfrac{a}{n+1}\big[x^{n+1}\big]_{p}^{q}$
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10.
Mathematics
For the quadratic 2x² + 6x − 1 = 0, find the sum and product of its roots.
Formula:Vieta's Formulas (roots)
$\alpha+\beta=-\dfrac{b}{a},\;\alpha\beta=\dfrac{c}{a}$
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11.
Quantitative Aptitude
Two fair dice are rolled. What is the probability that the sum of the numbers is 5?
Formula:Probability (two dice)
$P = \dfrac{\text{favourable}}{\text{total}}$
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12.
Quantitative Aptitude
The sum of the ages of two people is 50 years, and one is 4 years older than the other. Find their ages.
Formula:Ages (linear equations)
$x + (x+d) = S$
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13.
Mathematics
Find the binomial coefficient C(6, 2) — the coefficient of x^2 in (1 + x)^6.
Formula:Binomial Coefficient
$\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$
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14.
Quantitative Aptitude
Find the simple interest on $13,000 at 10% per annum for 4 year(s).
Formula:Simple Interest
$SI = \dfrac{P\times R\times T}{100}$
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15.
Quantitative Aptitude
An item is bought for $400 and sold for $560. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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16.
Quantitative Aptitude
Two varieties costing $27 and $82 per kg are mixed to give a mixture worth $50 per kg. Find the mixing ratio.
Formula:Alligation (Mixtures)
$\dfrac{q_1}{q_2} = \dfrac{p_2-m}{m-p_1}$
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17.
Quantitative Aptitude
Find the HCF and LCM of 8 and 34.
Formula:LCM & HCF
$\text{LCM}\times\text{HCF} = a\times b$
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18.
Quantitative Aptitude
The marked price of an item is $1,400. After a 15% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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19.
Quantitative Aptitude
Find the simple interest on $13,000 at 5% per annum for 4 year(s).
Formula:Simple Interest
$SI = \dfrac{P\times R\times T}{100}$
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20.
Quantitative Aptitude
What is 20% of 100?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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